(c) Fac­tor­ize: 3x -8y - 4xy + 6 Us­ing the group­ing method: The terms are re-ar­ranged such that both terms have the same com­mon fac­tor. 3x + 6 -8y - 4xy = (3x + 6) - (8y + 4xy) 3(x + 2) - 4y(2 + x) N.B. ( x + 2 ) is com­mon to both. =(x + 2) (3 - 4y) You may ex­pand the an­swer to en­sure that the an­swer is the same as the given ex­pres­sion. In­deed, this is re­quired if time al­lows.

(d) Fac­tor­ize: 25a2 - 9 b2 The dif­fer­ence of two squares method is used. As a re­minder, we must find the square root of 25a2 and 9b2. Since the square roots are 5a and 3b, re­spec­tively, then: 25a2 - 9b2 = (5a - 3b)(5a + 3b)

I am sure that you re­al­ize that (5a + 3b)(5a - 3b) is also cor­rect.

You must en­sure that you are fa­mil­iar with the four meth­ods, com­mon fac­tor, group­ing, qua­dratic fac­tors and dif­fer­ence of two squares demon­strated above, and know when to use each. You can­not af­ford to not earn the marks avail­able from these ques­tions.

You may check your an­swer by sub­sti­tut­ing the val­ues x = 3 and y = 2 into both equa­tions to

show that they sat­isfy the equa­tions.

Do you re­alise that in ex­am­ple 1, since the co­ef­fi­cients of y are - 2 and 2, re­spec­tively, in both equa­tions you elim­i­nate y by adding? If the co­ef­fi­cients are the same, that is, if the co­ef­fi­cients of y are both 2, then you elim­i­nate by sub­tract­ing.